Scala analysis: xen11-chalmers-tetrachordal-08-05
Transposition and Inversion by 2/B, 8 tones, an Octony
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 16/15 111.731285 minor diatonic semitone 3: 75/64 274.582429 classic augmented second 4: 135/112 323.352810 septimal wide minor third 5: 5/4 386.313714 major third 6: 4/3 498.044999 perfect fourth 7: 15/8 1088.268715 classic major seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 1125/1024 162.8511 double augmented prime 4: 36/35 48.7704 septimal diesis, 1/4-tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 16/15 111.7313 minor diatonic semitone 7: 45/32 590.2237 diatonic tritone 8: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 1125/1024 162.851 cents double augmented prime 1: 1 45/32 590.224 cents diatonic tritone 2: 2 16/15 111.731 cents minor diatonic semitone 2: 2 448/405 174.692 cents 2: 2 2025/1792 211.622 cents 2: 2 3/2 701.955 cents perfect fifth 3: 2 256/225 223.463 cents Neapolitan diminished third 3: 1 3645/3136 260.392 cents 3: 2 75/64 274.582 cents classic augmented second 3: 2 14/9 764.916 cents septimal minor sixth 3: 1 8/5 813.686 cents minor sixth 4: 2 135/112 323.353 cents septimal wide minor third 4: 2 5/4 386.314 cents major third 4: 2 8/5 813.686 cents minor sixth 4: 2 224/135 876.647 cents narrow septimal major sixth 5: 1 5/4 386.314 cents major third 5: 2 9/7 435.084 cents septimal major third, BP third 5: 2 128/75 925.418 cents diminished seventh 5: 1 6272/3645 939.608 cents 5: 2 225/128 976.537 cents augmented sixth 6: 2 4/3 498.045 cents perfect fourth 6: 2 3584/2025 988.378 cents 6: 2 405/224 1025.308 cents 6: 2 15/8 1088.269 cents classic major seventh 7: 1 64/45 609.776 cents 2nd tritone 7: 1 2048/1125 1037.149 cents double diminished octave 7: 2 15/8 1088.269 cents classic major seventh 7: 2 27/14 1137.039 cents septimal major seventh 7: 2 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.57143 = 32/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 63.0 111.7 274.6 323.4 386.3 498.0 1088.3 1200.0 63.0 : 48.8 211.6 260.4 323.4 435.1 1025.3 1137.0 1200.0 111.7 : 162.9 211.6 274.6 386.3 976.5 1088.3 1151.2 1200.0 274.6 : 48.8 111.7 223.5 813.7 925.4 988.4 1037.1 1200.0 323.4 : 63.0 174.7 764.9 876.6 939.6 988.4 1151.2 1200.0 386.3 : 111.7 702.0 813.7 876.6 925.4 1088.3 1137.0 1200.0 498.0 : 590.2 702.0 764.9 813.7 976.5 1025.3 1088.3 1200.0 1088.3: 111.7 174.7 223.5 386.3 435.1 498.0 609.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 590.2237 cents 175/128, 541.4533 cents 36/35, 48.7704 cents 2: 111.7313 .. 701.9550 cents 45/32, 590.2237 cents 512/675,-478.4924 cents 3: 223.4626 .. 813.6863 cents 45/32, 590.2237 cents 512/675,-478.4924 cents 4: 323.3528 .. 876.6472 cents 25088/18225, 553.2944 cents 675/896,-490.3335 cents 5: 386.3137 .. 976.5374 cents 45/32, 590.2237 cents 675/896,-490.3335 cents 6: 498.0450 .. 1088.2687 cents 45/32, 590.2237 cents 512/675,-478.4924 cents 7: 609.7763 .. 1151.2296 cents 175/128, 541.4533 cents 512/675,-478.4924 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 45/32, 590.2237 cents Average / Smallest step : 3.075637 Largest / Average step : 3.934825 Largest / Smallest step : 12.102093 Median interval of one step : 87.34609 cents, amount: 0 Least squares average step : 120.30050 cents, oct.: 962.40398 cents Scale is not proper Step pattern alph. order: ABCBADED Step pattern size order : BADABCEC Scale is not a Constant Structure Scale diversity : 1.494970 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 Rothenberg efficiency : 0.387500 redundancy: 0.612500 Efficiency x scale size : 3.100000 Number of different interval sizes : 28 = 4.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.57143 = 32/7 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 458752/455625, 11.8410 cents Most common intervals : 16/15, 111.7313 cents & inv., amount: 4 Most common triad is 0.0 111.731 1088.269 cents, amount: 2 Number of recognisable fifths : 2, average 701.9550 cents Scale contains a complete diamond : 1 15 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 37.5000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 6-7 -- Rational properties -- Prime limit : 7 Odd number limit : 3645 (O: 3645 U: 3645) Highest odd numerator or denominator: 135 Scale harmonicity : 0.015204 Average absolute harmonicity : 0.202934 Specific harmonicity : 0.112765 Fundamental : 1/60480, -15.8842 octaves, 0.0043 Hz. Guide tone : 75600, 16.2061 octaves, 19778892.737 Hz. Exponens Consonantiae : 4.572288E+09, 32.09027 octaves Euler's gradus suavitatis : 47 Sum of Mann's harmonic distance : 257.0, average 32.12500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.96503, average 1.12063 Sum of Tenney's harmonic distance : 17.87995, average 2.23499 Vogel's harmonic complexity : 28.75000 Wille's k value : 35437 Wilson's harmonic complexity : 47 Rectangular lattice diameter : 11 Triangular lattice diameter : 7 Lattice compactness : 172.08452, average 4.78013 Lattice compactness (without 2's) : 86.55334, average 2.40426 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -6 .. 4 -0.75000 24 1 3: -3 .. 3 0.00000 10 1 5: -1 .. 2 0.50000 6 4 7: -1 .. 1 0.00000 2 2 Average exponent except 2's : 4 / 8 = 0.50000 Average absolute exponent except 2's: 18 / 8 = 2.25000 Scale is weakly epimorphic with val: <8 12 17 22| Scale is weakly epimorphic with val: <8 12 21 22| Scale is weakly epimorphic with val: <8 12 21 23| Scale is weakly epimorphic with val: <8 13 17 20| Scale is weakly epimorphic with val: <8 13 21 24| Scale is weakly epimorphic with val: <8 14 19 23| Scale is weakly epimorphic with val: <8 14 19 24|
FIT/MODE
8: 0 0 2 0 0 1 4 1 N SD: 60.0648 c. M: 111.7313 c. 9: 0 1 1 0 1 1 4 1 N SD: 34.6517 c. M: 62.9609 c. 10: 1 0 1 1 0 1 5 1 N SD: 29.4686 c. M:-57.0391 c. 11: 1 0 2 0 1 1 5 1 N SD: 34.7962 c. M:-52.6903 c. 12: 1 0 2 0 1 1 6 1 N SD: 19.4605 c. M:-37.0391 c. 17: 1 1 2 1 0 2 8 2 N SD: 21.9580 c. M: 33.3725 c. 18: 1 1 2 1 1 1 9 2 N SD: 16.8864 c. M: 31.3783 c. 19: 1 1 2 1 1 2 9 2 N SD: 11.5697 c. M: 21.9508 c. 21: 1 1 3 1 1 2 10 2 N SD: 11.1933 c. M:-19.5043 c. 22: 1 1 3 1 1 2 11 2 N SD: 4.6731 c. M: 8.4154 c. 34: 2 1 5 1 2 3 17 3 N SD: 5.4618 c. M:-7.7705 c. 41: 2 2 5 2 2 4 20 4 N SD: 5.4487 c. M: 11.1678 c. 52: 3 2 7 2 3 5 25 5 N SD: 5.0070 c. M:-9.6473 c. 53: 3 2 7 2 3 5 26 5 N SD: 3.1603 c. M: 6.3717 c. 56: 3 2 8 2 3 5 28 5 N SD: 3.3681 c. M: 5.1879 c. 74: 4 3 10 3 4 7 36 7 N SD: 2.2935 c. M:-4.6577 c. 75: 4 3 10 3 4 7 37 7 N SD: 1.8931 c. M: 3.3528 c. 96: 5 4 13 4 5 9 47 9 N SD: 1.0904 c. M:-1.9550 c. 118: 6 5 16 5 6 11 58 11 N SD: 1.0116 c. M:-2.0709 c. 149: 8 6 20 6 8 14 73 14 N SD: 0.9989 c. M:-1.4686 c. 152: 8 6 21 6 8 14 75 14 N SD: 0.9215 c. M:-1.7334 c. 171: 9 7 23 7 9 16 84 16 N SD: 0.4885 c. M: 0.8982 c. 267: 14 11 36 11 14 25 131 25 N SD: 0.4695 c. M:-0.8314 c. 289: 15 12 39 12 15 27 142 27 N SD: 0.4152 c. M: 0.6772 c. 301: 16 12 41 12 16 28 148 28 N SD: 0.4159 c. M:-0.8265 c. 323: 17 13 44 13 17 30 159 30 N SD: 0.2162 c. M:-0.3402 c. 419: 22 17 57 17 22 39 206 39 N SD: 0.2215 c. M:-0.3579 c. 494: 26 20 67 20 26 46 243 46 N SD: 0.1294 c. M: 0.2759 c. 590: 31 24 80 24 31 55 290 55 N SD: 0.1268 c. M:-0.2601 c. 612: 32 25 83 25 32 57 301 57 N SD: 0.1042 c. M: 0.2158 c. 913: 48 37 124 37 48 85 449 85 N SD: 0.0793 c. M:-0.1278 c. 935: 49 38 127 38 49 87 460 87 N SD: 0.0631 c. M: 0.0771 c. 1106: 58 45 150 45 58 103 544 103 N SD: 0.0410 c. M: 0.0797 c. 1429: 75 58 194 58 75 133 703 133 N SD: 0.0411 c. M: 0.0744 c. 1525: 80 62 207 62 80 142 750 142 N SD: 0.0356 c. M:-0.0570 c. 2019: 106 82 274 82 106 188 993 188 N SD: 0.0201 c. M:-0.0406 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x 4 S SD: 101.9550 cents 3 x x x x x 4 x 6 S SD: 0.0000 cents 4 x x x x 5 x x 8 SD: 0.0000 cents 5 x x x 6 x 7:9:10 SD: 27.6007 cents 6 x x 7 x x 8:11:12 SD: 9.9157 cents 7 x x 8 x 9 x 13:14 SD: 16.8399 cents 8 x x 9 x 10:11:15:16 SD: 17.7004 cents 9 x 10 x 11 x 12:17:18 SD: 15.1479 cents 10 x 11 x 12 x 13:19:20 SD: 14.6211 cents 11 x 12:13 x 14:15:21:22 SD: 12.0040 cents 12 x 13:14 x 15:16:23:24 SD: 7.8666 cents 13 x 14:15 x 16:17:24:26 SD: 9.9526 cents 14 x 15:16:17:18:19:26:28 SD: 10.7845 cents 15 x 16 x 18:19:20:28:30 SD: 4.2320 cents 16 x 17:19 x 20:21:30:32 SD: 6.0439 cents 17 x 18:20 x 21:23:32:34 SD: 6.0406 cents 18 x 19:21:22:23:24:34:36 SD: 7.2532 cents 19 x 20:22:23:24:25:36:38 SD: 6.6937 cents 20:21 x 23:24:25:27:38:40 SD: 7.2485 cents 21:22 x x 25:26:28:39:42 SD: 6.0561 cents 22:23 x 26:27:28:29:41:44 SD: 7.6375 cents 23:24:25:27:28:29:31:43:46 SD: 5.7066 cents 24:25:26:28:29:30:32:45:48 SD: 3.6606 cents 28:29:30:33:34:35:37:53:56 SD: 3.6126 cents 29:30:31:34:35:36:39:54:58 SD: 2.9196 cents 45:47:48:53:54:56:60:84:90 SD: 2.5184 cents 47:49:50:55:57:59:63:88:94 SD: 2.3999 cents 48:50:51:56:58:60:64:90:96 SD: 1.6913 cents 57:59:61:67:69:71:76:107:114 SD: 1.6133 cents 63:65:67:74:76:79:84:118:126 SD: 1.5650 cents 75:78:80:88:90:94:100:141:150 SD: 1.4308 cents 77:80:82:90:93:96:103:144:154 SD: 1.3848 cents 87:90:93:102:105:109:116:163:174 SD: 0.9287 cents 104:108:111:122:125:130:139:195:208 SD: 0.8975 cents 105:109:112:123:127:131:140:197:210 SD: 0.8957 cents 117:121:125:137:141:146:156:219:234 SD: 0.8833 cents 132:137:141:155:159:165:176:248:264 SD: 0.7266 cents 135:140:144:158:163:169:180:253:270 SD: 0.5715 cents 180:187:192:211:217:225:240:338:360 SD: 0.5070 cents 192:199:205:225:231:240:256:360:384 SD: 0.4692 cents 209:217:223:245:252:261:279:392:418 SD: 0.4419 cents 239:248:255:280:288:299:319:448:478 SD: 0.3388 cents 240:249:256:281:289:300:320:450:480 SD: 0.3035 cents 272:282:290:319:328:340:363:510:544 SD: 0.3005 cents 273:283:291:320:329:341:364:512:546 SD: 0.2485 cents 297:308:317:348:358:371:396:557:594 SD: 0.2077 cents 360:373:384:422:434:450:480:675:720 SD: 0.2067 cents 408:423:435:478:492:510:544:765:816 SD: 0.1588 cents 511:530:545:599:616:639:681:958:1022 SD: 0.1585 cents 512:531:546:600:617:640:683:960:1024 SD: 0.1292 cents 600:622:640:703:723:750:800:1125:1200 SD: 0.1076 cents